1. Field of the Invention
The present invention generally relates to the field of computed tomography imaging, and in particular, to a method, apparatus, and computer-readable medium for pre-reconstruction decompositions in dual energy computed tomography.
2. Discussion of the Background
The mathematics used in CT-reconstruction were first elucidated by Johann Radon in 1917. Once you can reduce the measured transmitted measurements to line integrals (also called the Radon transform), Radon showed how to invert the integrals (i.e., using the inverse Radon transform) to uniquely determine the integrand: a function the describes properties of interest; in this case, the linear attenuation coefficients of the various tissues in the patient.
An exact solution requires monochromatic radiation. However, all practical sources of X rays at present are polychromatic. Using an inverse Radon transform method such as filtered backprojection, may result in strong artifacts in the reconstructed image known as beam hardening artifacts (beam hardening, because as the polychromatic beam transverses the patient, the softer—lower energy—photons are preferentially absorbed or scattered out of the beam, leaving the harder photons). It is worth noting that the Radon transform and it inverse are linear equations. The beam hardening makes them nonlinear and not exactly solvable.
A possible solution to this problem is to perform a dual energy scan (i.e., scan the same object with two polychromatic scans but one at a higher energy than the other). A dual-energy computed tomography (CT) technique may generate images having reduced beam hardening artifacts and may provide some information regarding the composition of the object being imaged, for example as discussed in Alvarez, R. and A, Macovski., “Energy-selective reconstruction in x-ray computerized tomography”, Phys. Med. Biol., 21, 733-744, 1976, which is incorporated herein by reference in its entirety. Dual-energy CT has been applied to bone mineral to bone mineral quantification (e.g., as discussed in D. D. Faul, J. L. Cauch, C. E. Cann, A. Laval-Jeantet, D. P. Boyd, and H. K. Genant, “Composition-selective reconstruction using dual energy CT for bone mineral quantification”, J. Comput. Assist. Tomography, 6, 202-204, 1982, which is incorporated herein by reference in its entirety), attenuation correction in nuclear medicine (e.g., as discussed in H. Hasegawa, T. F. Lang, K. J. Brown, E. L. Gingold, S. M. Reilly, S. C. Blankespoor, S. C. Liew, B. M. W. Tsui, and C. Ramanathan, “Object-specific attenuation correction of SPEC with correlated dual-energy X-ray CT”, IEEE Trans. Nucl. Sci., 40, 1212-52, 1993, which is incorporated herein by reference in its entirety), bone subtraction, and contrast enhancement between lesion or fatty and healthy tissue. It may find new applications in molecular imaging with a new contrast agent (e.g., as discussed in F. Hyafil, J. Cornily, J. E. Feig, R. Gordon, E. Vucic, V. Amirbekian, E. A. Fisher, V. Fuster, L. J. Feldman, and Z. A. Fayad, “Noninvasive detection of macrophages using a nanoparticulate contrast agent for computed tomography”, Nature Medicine, 13,636-641, 2007, which is incorporated herein by reference in its entirety). The polynomial approximation methods are widely used in the pre-reconstruction decomposition.
Thus, background methods of dual-energy CT may reconstruct images having reduced beam hardening artifacts by performing pre-reconstruction decomposition. The projections of imaged subjects are related to the line integral of the two basis materials, e.g. bone and water, or two components of photon absorptions, i.e. photoelectric and Compton processes through non-linear equations. Usually, the projections are fitted into polynomials of the line integrals. From the measured projection data, the line integrals can be obtained by solving the polynomials. Other methods, such as the variation method, the sub-region method, and the iso-transmission method can also be used in the decompositions. The basis images then can be generated from the resulting line integrals by a conventional reconstruction algorithm. The effective Z, density, and monochromatic images can be obtained by combining the basis images.
However, as discussed in K. Chuang and H. K. Huang, “Comparison of four dual energy image decomposition methods”, Phys. Med. Biol., 33, 455-466, 1988, which is incorporated herein by reference in its entirety, the direct polynomial approximation is not accurate and the indirect polynomial approximation has some computational drawbacks.
In particular, background pre-reconstruction decomposition methods may described as follows:
Polynomial Method
The measured projection data at low and high voltages are written as two polynomials of the line integrals of basis materials. The coefficients in the polynomials are obtained by fitting to the calibration measurements. The line integrals are calculated by use of the Newton-Raphson iteration method.
Direct Polynomial Method
The line integrals of the two basis materials are approximated with two polynomials of the measured projection data. The coefficients in the polynomials are obtained by fitting to the calibration measurements. From the measured projection data, the line integrals can be obtained directly.
Sub-region Method
This method is an improvement of the direct polynomial method. The projections are divided into many sub-regions and the coefficients of the polynomials are tuned up for each sub-region.
Iso-transmission Method
The projection data are written as a linear function of the line integrals. The so called regression coefficients in the function depend on the projection data. These coefficients are predefined on a set of projection values through a calibration procedure. For any projection value within the limit of the calibration table, an interpolation procedure is adopted to obtain the regression coefficients. Finally, the line integrals are obtained by solving the linear equations.
Variation Method
A cost function is defined as a sum of square difference between the measured projection and the predicted projection as a function of line integrals. Finding the minimum of the cost function with certain constraints, one can determine the line integrals.